Minimum Satisfying Assignments for SMT

  • Isil Dillig
  • Thomas Dillig
  • Kenneth L. McMillan
  • Alex Aiken
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7358)


A minimum satisfying assignment of a formula is a minimum-cost partial assignment of values to the variables in the formula that guarantees the formula is true. Minimum satisfying assignments have applications in software and hardware verification, electronic design automation, and diagnostic and abductive reasoning. While the problem of computing minimum satisfying assignments has been widely studied in propositional logic, there has been no work on computing minimum satisfying assignments for richer theories. We present the first algorithm for computing minimum satisfying assignments for satisfiability modulo theories. Our algorithm can be used to compute minimum satisfying assignments in theories that admit quantifier elimination, such as linear arithmetic over reals and integers, bitvectors, and difference logic. Since these richer theories are commonly used in software verification, we believe our algorithm can be gainfully used in many verification approaches.


Propositional Logic Satisfying Assignment Partial Assignment Predicate Abstraction Linear Arithmetic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Isil Dillig
    • 1
  • Thomas Dillig
    • 1
  • Kenneth L. McMillan
    • 2
  • Alex Aiken
    • 3
  1. 1.College of William & MaryUSA
  2. 2.Microsoft ResearchUSA
  3. 3.Stanford UniversityUSA

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